Strength of Shafts. 417 Example 16.—A foundation bolt with square head (Fig. 368) is secured by a cotter. Find D, b, and / in terms of d> where ft,fs, andyi vary as I : | : 2 respectively. (Hons. Mach. Constr. Exam. 1886.) Following the previous calculations : D = ro8 d, b = 1-44 d^ and t—"*f>z d. 368. Torsional Stress-Action unallied with bending occurs only in very short shafts. In any case the two actions Ihust be separately considered. Fig. 369 shews a shaft under twist, the external load being caused by the couple dxb c, while the in- ternal resistance of the shaft is shewn by the couple exfg* .-. External mometitjlmoment of resistance of section or W>=/sZt where Zt, the modulus of section, is a number depending on the size and shape of the section. Strength of Solid Round Shaft.—Let r be the outer radius of a solid shaft, Fig. 370. Imagining the section divided into concentric rings: Total stress on outer ring =/s X2irrxt (i) Bntfs diminishes towards the centre because l>5 decreases: .-. Total stress at any other ring ^ = -±fs x 21?^ x t (2) * A couple is formed by a pair of equal and opposite forces, and can pro- duce turning effect only, being represented by 'one force x "total arm.'